Search results for "Randomized algorithm"
showing 10 items of 11 documents
Do Randomized Algorithms Improve the Efficiency of Minimal Learning Machine?
2020
Minimal Learning Machine (MLM) is a recently popularized supervised learning method, which is composed of distance-regression and multilateration steps. The computational complexity of MLM is dominated by the solution of an ordinary least-squares problem. Several different solvers can be applied to the resulting linear problem. In this paper, a thorough comparison of possible and recently proposed, especially randomized, algorithms is carried out for this problem with a representative set of regression datasets. In addition, we compare MLM with shallow and deep feedforward neural network models and study the effects of the number of observations and the number of features with a special dat…
Randomized renaming in shared memory systems.
2021
Abstract Renaming is a task in distributed computing where n processes are assigned new names from a name space of size m . The problem is called tight if m = n , and loose if m > n . In recent years renaming came to the fore again and new algorithms were developed. For tight renaming in asynchronous shared memory systems, Alistarh et al. describe a construction based on the AKS network that assigns all names within O ( log n ) steps per process. They also show that, depending on the size of the name space, loose renaming can be done considerably faster. For m = ( 1 + ϵ ) ⋅ n and constant ϵ , they achieve a step complexity of O ( log log n ) . In this paper we consider tight as well as loos…
Separations in Query Complexity Based on Pointer Functions
2015
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function $f$ on $n=2^k$ bits defined by a complete binary tree of NAND gates of depth $k$, which achieves $R_0(f) = O(D(f)^{0.7537\ldots})$. We show this is false by giving an example of a total boolean function $f$ on $n$ bits whose deterministic query complexity is $\Omega(n/\log(n))$ while its zero-error randomized query complexity is $\tilde O(\sqrt{n})$. We further show that the quantum query complexity of the same function is $\tilde O(n^{1/4})$, giving the first example of a total function with a super-quadra…
Fast computation of abelian runs
2016
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\sigma$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\sigma+p)$, where $p$ is the norm of $\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p$ in $w$ in time $O(np)$, for any given norm $p$. Finally, we give an $O(n^2)$-time offline randomi…
Forrelation
2014
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum query, yet we show that any randomized algorithm needs Ω(√(N)log(N)) queries (improving an Ω(N[superscript 1/4]) lower bound of Aaronson). Conversely, we show that this 1 versus Ω(√(N)) separation is optimal: indeed, any t-query quantum algorithm whatsoever can be simulated by an O(N[superscript 1-1/2t])-query randomized algorithm. Thus, resolving an open questi…
Exact simulation of first exit times for one-dimensional diffusion processes
2019
International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …
Frequency Prediction of Functions
2012
Prediction of functions is one of processes considered in inductive inference. There is a "black box" with a given total function f in it. The result of the inductive inference machine F( ) is expected to be f(n+1). Deterministic and probabilistic prediction of functions has been widely studied. Frequency computation is a mechanism used to combine features of deterministic and probabilistic algorithms. Frequency computation has been used for several types of inductive inference, especially, for learning via queries. We study frequency prediction of functions and show that that there exists an interesting hierarchy of predictable classes of functions.
A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems
2005
This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures.
Reactive GRASP for the strip-packing problem
2008
This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite height so as to minimize the required height. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances which have been previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures. The results show that the GRASP algorithm outperforms recently reported metaheuristics.
Active Learning of Recursive Functions by Ultrametric Algorithms
2014
We study active learning of classes of recursive functions by asking value queries about the target function f, where f is from the target class. That is, the query is a natural number x, and the answer to the query is f(x). The complexity measure in this paper is the worst-case number of queries asked. We prove that for some classes of recursive functions ultrametric active learning algorithms can achieve the learning goal by asking significantly fewer queries than deterministic, probabilistic, and even nondeterministic active learning algorithms. This is the first ever example of a problem where ultrametric algorithms have advantages over nondeterministic algorithms.